As a method of detecting the cetane number associated with this type of apparatus, a method which uses the ignition timing of fuel has been suggested in a patent document 1 or the like. Specifically, in the patent document 1 or the like, after a lapse of predetermined time after the internal combustion engine is in a fuel cut state (hereinafter referred to as F/C, as occasion demands), fuel for detecting the cetane number is injected in a particular injection pattern. Then, the cetane number is detected by the measured ignition timing after the lapse of predetermined time.    Patent Document 1: Japanese Patent Application Laid Open No. 2005-344557    Patent Document 2: Japanese Patent Application Laid Open No. 2006-226188    Patent Document 3: Japanese Patent Application Laid Open No. 2006-16994    Patent Document 4: Japanese Patent Application Laid Open No. 2005-320872    Patent Document 5: Japanese Patent Application Laid Open No. 2006-183581    Patent Document 6: Japanese Patent Application Laid Open No. Hei 11-107771